Myopic deterrence policies and the instability of equilibria

We develop a general equilibrium model of crime in which honest workers face an effective tax rate on earnings, consisting of an exogenous income tax, used to pay for policing, and an endogenous crime tax, given by the proportion of their disposable income that is stolen. When there are two stable equilibria, the low crime equilibrium is welfare dominant and, furthermore, welfare is a decreasing function of the income tax rate. However, as the income tax rate is reduced, the degree of stability of the low crime equilibrium diminishes, until for sufficiently low tax rates, the low crime equilibrium is unstable with respect to any small, positive perturbation in the crime rate. Thus myopic maximization of social welfare exposes the economy to random shocks in the crime rate that can destroy the preferred, low crime equilibrium. We argue that this dilemma between economizing on resources used for deterrence and ensuring the stability of the most desirable equilibrium is a fundamental trade-off in the design of many institutions intended to control antisocial behavior, including rent-seeking, corruption and theft.